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%I #22 Feb 28 2024 02:09:23
%S 5,60,540,4320,32400,233280,1632960,11197440,75582720,503884800,
%T 3325639680,21767823360,141490851840,914248581120,5877312307200,
%U 37614798766080,239794342133760,1523399350026240,9648195883499520,60935974001049600,383896636206612480
%N a(n) = 5*n*6^(n-1).
%C Main transitions in systems of n particles with spin 5/2.
%C Refer to the general explanation in A212697.
%C This particular sequence is obtained for base b=6, corresponding to spin S=(b-1)/2=5/2.
%C n*(b-1)*b^(n-1): for this sequence, set b=6.
%C Arithmetic derivative of 6^n: a(n) = A003415(6^n). [_Bruno Berselli_, Oct 22 2013]
%H Stanislav Sykora, <a href="/A212700/b212700.txt">Table of n, a(n) for n = 1..100</a>
%H Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36)
%F G.f. 5*x / (6*x-1)^2. a(n) = 5*A053469(n). - _R. J. Mathar_, Oct 15 2013
%t Rest@ CoefficientList[Series[5 x/(6 x - 1)^2, {x, 0, 18}], x] (* or *)
%t Array[5 # 6^(# - 1) &, 18] (* _Michael De Vlieger_, Nov 18 2019 *)
%o (PARI): mtrans(n, b) = n*(b-1)*b^(n-1);
%o for (n=1, 100, write("b212700.txt", n, " ", mtrans(n, 6)))
%Y Cf. A001787, A212697, A212698, A212699, A212701, A212702, A212703, A212704 (b = 2, 3, 4, 5, 7, 8, 9, 10).
%Y Cf. A003415, A053469.
%K nonn,easy
%O 1,1
%A _Stanislav Sykora_, May 25 2012
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